GATE DA Artificial Intelligence Quiz

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Question 1

Let x and y be two propositions. Which of the following statements is a tautology / are tautologies ?
(GATE DA 2024 - MSQ) [1 Marks]

 


  • (~x ∧ y )=> (y=>x)

  • (x ∧ ~y) =>(~x=>y)

  • (~x ∧ y)=>(~x=>y)

  • (x βŸ‘ ~y)=>(y=>x)

Question 2

Consider performing depth-first search (DFS) on an undirected and unweighted graph G starting at vertex 𝑠. For any vertex 𝑒 in G, 𝑑[𝑒] is the length of the shortest path from 𝑠 to 𝑒. Let (𝑒,𝑣) be an edge in G such that 𝑑[𝑒]<𝑑[𝑣]. If the edge (𝑒,𝑣) is explored first in the direction from 𝑒 to 𝑣 during the above DFS, then (𝑒,𝑣) becomes a ______ edge.

  • Tree

  • Cross

  • Back

  • Grey

Question 3

Consider a state space where the start state is number 1. The successor function for the state numbered n returns two states numbered n+1 and n+2. Assume that the states in the unexpanded state list are expanded in the ascending order of numbers and the previously expanded states are not added to the unexpanded state list. Which ONE of the following statements about breadth-first search (BFS) and depth-first search (DFS) is true, when reaching the goal state number 6?
(GATE DA 2024 - MCQ) [2 Marks]

  • BFS expands more states than DFS.

  • DFS expands more states than BFS.

  • Both BFS and DFS expand equal number of states

  • Both BFS and DFS do not reach the goal state number 6

Question 4

Let game(ball, rugby) be true if the ball is used in rugby and false otherwise. Let shape(ball, round) be true if the ball is round and false otherwise. Consider the following logical sentences:

s1: βˆ€ball Β¬ game(ball, rugby) ⟹shape(ball, round)

s2: βˆ€ball Β¬ shape(ball, round) ⟹game(ball, rugby)

s3: βˆ€ball game(ball, rugby) ⟹ Β¬ shape(ball, round)

s4: βˆ€ball shape(ball, round) ⟹ Β¬ game(ball, rugby)

Which of the following choices is/are logical representations of the assertion,

β€œAll balls are round except balls used in rugby”?
(GATE DA 2024 - MSQ) [2 Marks]

  • 𝑠1 ∧ 𝑠3

  • s1 ∧ 𝑠2

  • 𝑠2 ∧ 𝑠3

  • 𝑠3 ∧ 𝑠4

Question 5

Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables:

GATE-DA-PYQ-2024-4

The value of 𝑃(π‘ˆ = 1, 𝑉 = 1, π‘Š = 1,𝑍 = 1) = ______ (rounded off to three decimal places).

  • 0.135

  • 0.150

  • 0.341

  • 0.125

Question 6

Let β„Ž1 and β„Ž2 be two admissible heuristics used in 𝐴 βˆ— search. Which ONE of the following expressions is always an admissible heuristic?
(GATE DA 2024 - MCQ) [1 Marks]

  • β„Ž1 + β„Ž2

  • β„Ž1 Γ— β„Ž2

  • β„Ž1 /β„Ž2, (β„Ž2 β‰  0)

  • |β„Ž1 βˆ’ β„Ž2|

Question 7

Consider the following statement: In adversarial search, 𝛼– 𝛽 pruning can be applied to game trees of any depth where 𝛼 is the (m) value choice we have formed so far at any choice point along the path for the MAX player and 𝛽 is the (n) value choice we have formed so far at any choice point along the path for the MIN player. Which ONE of the following choices of (m) and (n) makes the above statement valid?
(GATE DA 2024 - MCQ) [1 Marks]

  • (m) = highest, (n) = highest

  • (m) = lowest, (n) = highest

  • (m) = highest, (n) = lowest

  • (m) = lowest, (n) = lowest

Question 8

Let p and q be any two propositions. Consider the following propositional statements.

S1 : p β†’ q, S2 : Β¬p ∧ q, S3 : Β¬p ∨ q, S4 : Β¬p ∨ Β¬q,

where ∧ denotes conjunction (AND operation), ∨ denotes disjunction (OR operation), and Β¬ denotes negation (NOT operation). Which one of the following options is correct? (Note: ≑ denotes logical equivalence)

(GATE DA 2025 - MCQ) [1 Marks]

  • S1 ≑ S3

  • S2 ≑ S3

  • S2 ≑ S4

  • S1 ≑ S4

Question 9

Which of the following statements is/are correct in a Bayesian network?
(GATE DA 2025 - MSQ) [1 Marks]

  • Variable elimination is an approximate inference algorithm

  • Gibbs sampling is an exact inference algorithm

  • Variable elimination is used to determine conditional probabilities

  • Rejection sampling is an approximate inference algorithm

Question 10

Consider game trees Tree-1 and Tree-2 as shown. The first level is a MAX agent and the second level is a MIN agent. The value in the square node is the output of the utility function.

1
.

For what ranges of x and y, the right child of node B and the right child of node E will be pruned by alpha-beta pruning algorithm?

(GATE DA 2025 - MCQ) [2 Marks]

  • x ∈ [1, ∞) and y ∈ (βˆ’βˆž, 2]

  • x ∈ (βˆ’βˆž, 2] and y ∈ (βˆ’βˆž, 5]

  • x ∈ (βˆ’βˆž, 2] and y ∈ [2, ∞)

  • x ∈ [1, ∞) and y ∈ (βˆ’βˆž, 5]

There are 11 questions to complete.

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